Bayesian nonparametric methods have experienced a huge development in the last two decades, often standing out for their flexibility and coherent probabilistic foundations; see the monographs by [1]} and [2]} for recent stimulating accounts.
The cornerstone of Bayesian nonparametrics is the model based on the Dirichlet process [3]}, which can be expressed as
\(X_i \mid \tilde{P} \stackrel{\mbox{\scriptsize {iid}}}{\sim }\tilde{P}\)  and \( \tilde{P}\sim \text{DP}(\alpha , Q_0)\) ,
where \(\alpha > 0\)  is the concentration parameter and \(Q_0\)  is the baseline distribution over the sample space \((\mathbb {X}, \mathcal {X})\) .
The success of the Dirichlet process in actual implementations of the Bayesian approach to nonparametric problems is mostly due to its mathematical tractability, which is highlighted by conjugacy, and flexibility, which is assessed in terms of its large topological support.
